Subscriber access provided by A.A. Lemieux Library | Seattle University
Article
Dielectric Relaxation and Solvation Dynamics in a RoomTemperature Ionic Liquid: Temperature Dependence Youngseon Shim, and Hyung J Kim J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp406353j • Publication Date (Web): 26 Aug 2013 Downloaded from http://pubs.acs.org on August 31, 2013
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Dielectric Relaxation and Solvation Dynamics in a Room-Temperature Ionic Liquid: Temperature Dependence Youngseon Shim1 and Hyung J. Kim2,3,∗ 1 Samsung 2 Department 3 School
Advanced Institute of Technology, SEC, Yongin 446-712, Korea
of Chemistry, Carnegie Mellon University, Pittsburgh, PA 15213, USA
of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-722, Korea
Abstract Dielectric relaxation, related polarization and conductivity, and solvation dynamics of the ionic liquid, 1-butyl-3-methylimidazolium hexafluorophosphate (BMI+ PF− 6 ), are studied via molecular dynamics computer simulations in the temperature range 300 K ≤ T ≤ 500 K. Two main bands of its dielectric loss spectrum show differing temperature behaviors. As T increases, the absorption band in the microwave region shifts to higher frequencies rapidly, whereas the location of the bi-modal far-IR band remains nearly unchanged. Their respective intensities tend to decrease and increase. The static dielectric constant of BMI+ PF− 6 is found to decrease weakly with T . The ultrafast inertial component of solvation dynamics becomes, in general, slower while their dissipative relaxation component becomes faster. Roles played by ion reorientations and translations in governing dynamic and static dielectric properties of the ionic liquid are examined. A brief comparison with available experimental results is also made.
Keywords: ionic liquids, dielectric relaxation, dielectric loss spectrum, static dielectric constant, solvatochromism, solvation dynamics ∗
Corresponding author. Permanent address: Carnegie Mellon University. Email:
[email protected].
1
1
INTRODUCTION
Dielectric relaxation of room-temperature ionic liquids (RTILs) consisting of bulky organic cations paired with various types of anions has received a significant experimental and theoretical attention recently. Considerable efforts via microwave1–9 and tera-Hertz timedomain5–7, 10–13 spectroscopies and via molecular dynamics (MD) simulations14–22 have been directed towards understanding the respective roles played by translational and reorientational dynamics of RTIL ions and the contributions of their electric charge and dipole moments to the dielectric constant. Potential connections between dielectric relaxation and solvation dynamics have also been examined.18, 23–32 Due to strong electrostatic interactions with ion charges, polar molecules are well stabilized when solvated in RTILs. As such, empirical polarity scale33–35 of ionic liquids, which gauges their solvating power, is often comparable to and even exceeds that of highly dipolar solvents, e.g., acetonitrile, according to many experimental36–45 and simulation46–48 studies. Despite this, static dielectric constant ε0 of RTILs is not high; its typical value ranges between 10 and 15.49 Since RTIL ions are free charges, cations and anions subject to an external electric field tend to separate from each other and shield the external field, so that the net electric field inside the RTIL medium vanishes. This rearrangement of ion monopolar charges via translations, while crucial to solvation in RTILs,48, 50–52 often plays a minor role in ε0 at room temperature. Recent MD simulations indeed demonstrated that RTIL monopolar charges make a small but positive contribution to ε0 .17, 18 The ion dipoles on the other hand tend to align to the external field through reorientations, resulting in local dipole density. Therefore if the RTIL ions are characterized by significant center-of-mass dipole moments, their reorientations are the main contributor to ε0 at room temperature. The influence of temperature T on ε0 has also been studied experimentally. In general, ε0 of RTILs shows a rather weak dependence on T . For example, Yao and coworkers found that the dielectric constant of BMI+ PF− 6 declines only slightly from ε0 = 12.3 to 11.7 in the temperature range 300 K ≤ T ≤ 360 K.7 A somewhat stronger diminution in ε0 from 16.7 at 288 K to 13.0 at 338 K was obtained by Buchner, Hefter and coworkers for the same ionic liquid.6 Weing¨artner and coworkers found that ε0 of a similar BMI+ -based RTIL essentially does not change with temperature for 280 K ≤ T ≤ 320 K.49 By contrast, DC conductivity of RTILs increases substantially with T .7, 53–56 In this article, we study dielectric and conductivity behaviors of BMI+ PF− 6 and their temperature dependence via MD simulations. The overall static dielectric constant is found to decrease slowly with growing T . Of essential importance is the antagonistic roles played 2
by the translations of ion charges and reorientations of ion dipoles, which tend to increase and decrease ε0 , respectively, as T rises. The hindered librational and dissipative relaxation dynamics of RTIL translations lead to significant bi-modal dielectric loss in the tera-Hertz region. Interestingly, the position of this band changes little with T . By contrast, dielectric absorption in the microwave region via ion reorientational dynamics shifts to higher frequencies markedly as T increases. The outline of this paper is as follows: The theoretical formulation of dielectric relaxation in ionic systems is reviewed briefly in sec 2. A brief description of the models and methods employed in the present study is given in sec 3. Dielectric relaxation, related polarity and conductivity, and solvation dynamics of BMI+ PF− 6 and their variations with temperature are analyzed in sec 4. Section 5 concludes.
2
THEORETICAL BACKGROUND
Here we give a brief review of the theoretical formulation we employ to analyze MD results for dielectric relaxation of BMI+ PF− 6 . For details, the reader is referred to refs 15 and 18. In linear response theory, the electric susceptibility χ(ω) defined via Z ∞ Z t X 1 iωt χ(ω) = dt e χ(t) ; M tot (t) = dt0 χ(t − t0 )E(t0 ) ; M tot = qi,α r i,α , (1) V 0 −∞ i,α is related to the generalized dielectric constant ε(ω) and conductivity σ(ω) as 4πχ(ω) = ε0 (ω) + iε00 (ω) − 1 = i
4π 0 [σ (ω) + iσ 00 (ω)] , ω
(2)
where prime and double prime represent, respectively, the real and imaginary parts of ε(ω) and σ(ω). In eq 1, M tot (t) is the average total dipole moment of the system at time t induced by a homogeneous electric field E(t), V is the volume, qi,α and r i,α are, respectively, the charge and position of the site i of ion α, and the sum is taken over charge sites of all ions. In view of the non-vanishing DC conductivity of ionic systems, i.e., σ(0) = σ 0 (0) 6= 0, we also consider the non-divergent part εc (ω) of the dielectric constant 4π σ(0) εc (ω) ≡ ε(ω) − i σ(0) = 1 + 4π χ(ω) − i . ω ω We note that experimentally, the static dielectric constant ε0 is determined as1, 23, 57, 58 4π ε0 = εc (0) = lim ε(ω) − i σ(0) . ω→0 ω 3
(3)
(4)
The fluctuation-dissipation theorem59 relates χ(ω) to the time correlation of M tot as Z ∞ 1 dΦMM (t) χ(ω) = − ; ΦMM (t) = hM tot (t)·M tot (0)i , (5) dt eiωt 3V kB T 0 dt where kB is Boltzmann’s constant. For convenience, we decompose M tot into its rotational and translational components15, 18 cm M tot = M cm rot + M tr ;
M cm rot ≡
X
µcm,α ;
M cm tr ≡
X
α
µcm,α =
X
qα r cm,α ;
α
qi,α (r i,α − r cm,α ) ;
i∈α
qα =
X
qi,α ,
(6)
i∈α
where qα and r cm,α are the net charge and the position of the center of mass of ion α, and µcm,α is its dipole moment defined with respect to its center of mass. χ(ω) in eq 5 can then be expressed as15 cm χ(ω) = χcm 1 (ω) + χ2 (ω) ; Z ∞ o 1 n cm 2 cm cm χ1 (ω) = hM rot i + dt eiωt [ iω Φcm (t) + Φ (t)] ; MM MJ 3V kB T 0 Z ∞ 1 i cm iωt cm cm dt e χ2 (ω) = − ΦJM (t) + ΦJJ (t) ; 3V kB T 0 ω cm cm Φcm MM (t) = hM rot (t)·M rot i ;
cm cm Φcm JJ (t) = hJ tr (t)·J tr i ;
cm cm Φcm MJ (t) = hM rot (t)·J tr i ;
cm cm Φcm JM (t) = hJ tr (t)·M rot i ,
where J tr is the current arising from the translational motions of ion center-of-mass X d cm qα r˙ cm,α , M = J cm ≡ tr dt tr α
(7)
(8)
cm and the cross-correlation functions satisfy Φcm JM (t) = −ΦMJ (t). To avoid confusion, we men-
tion that though ion reorientational motions about their center of mass are the main contributor to M cm rot , their internal vibrations also make a contribution. cm We also introduce εcm rot (ω) and εtr (ω) associated primarily with reorientations with respect
to, and translations of, the center-of-mass of individual ions following our previous study18 σ(0) cm cm cm cm cm εrot (ω) ≡ 1 + 4πχ1 (ω) ; εtr (ω) ≡ εc (ω) − εrot (ω) = 4π χ2 (ω) − i . (9) ω
3
SIMULATION METHODS
+ The simulation cell comprises 128 pairs of BMI+ and PF− 6 ions. For BMI , we used the fully
flexible all-atom description of refs 60 and 61, based on OPLS-AA62–64 and AMBER65–67 force 4
fields. For PF− 6 , we employed the Lennard-Jones (LJ) parameters and charge assignments of ref 64 and intramolecular vibrational force constants of ref 68. We note that the same RTIL 69 potential model was used in our previous work on solvation in BMI+ PF− 6 -CO2 mixture. ˚ was employed as a For solvation simulations, a rigid diatomic molecule of bond length 3.5 A
probe solute. As in many of our prior studies,46, 47, 70 the solute LJ parameters, σ = 4 ˚ A and /kB = 100 K, and mass of 100 amu are identical for each constituent atom. We considered two different charge distributions for the solute: a neutral pair (NP) with no charges and an ion pair (IP) with ±1e assigned to its two constituent atoms, where e is the elementary charge. The latter yields a solute dipole moment of 16.7 D. The DL POLY program71 was used in all simulations. Periodic, cubic boundary conditions were employed. The long-range electrostatic interactions were computed via the Ewald method,72 resulting in essentially no truncation of these interactions. The trajectories were integrated via the Verlet leapfrog algorithm using a time step of 2 fs. We first performed NP T ensemble simulations at 1 atm to determine the solvent densities at different tempera−3 tures. BMI+ PF− 6 densities thus obtained are ρ = 1.349, 1.305, 1.265, 1.231, and 1.228 g cm
at T = 300, 350, 400, 450, and 500 K, in reasonable accord with measurements.73, 74 At each temperature (and density), N V T simulations were carried out with 10 ns equilibration after annealing from 800 K, followed by a 60 ns trajectory from which averages were computed. At 300 and 350 K, we performed the production simulation for 180 and 120 ns, respectively, to obtain good MD statistics for dielectric calculations. As for solvation study, we performed simulations for 30 ns after 10 ns equilibration, employing the rigid diatomic molecule described above as a probe solute.
4
RESULTS AND DISCUSSIONS
4.1
Dielectric relaxation and ion conductivity
We begin by considering dielectric relaxation in BMI+ PF− 6 in Figure 1. We mention at the outset that according to the simulation results, the contribution of the cross-correlations cm cm cm Φcm JM (t) and ΦMJ (t) to the susceptibilities, χ1 (ω) and χ2 (ω), in eq 7 is much smaller than cm cm cm cm cm that of Φcm MM (t) or ΦJJ (t). Therefore χ1 (ω) and χ2 (ω) and thus εrot (ω) and εtr (ω) in eq 9
arise mainly from decoupled motions, viz., reorientations with respect to, and translations of, the center-of-mass of individual ions, respectively. This state of affairs is very similar to the 1-ethyl-3-methylimidazolium case we investigated previously.18 With this in mind, we first consider εcm rot (ω) in Figure 1a. 5
Dielectric absorption in
cm BMI+ PF− 6 induced by its M rot occurs in the microwave region. As T increases, this band
shifts to higher frequencies rapidly while the overall amplitude of εcm rot (ω) decreases. The 00 frequency at the maximum intensity, i.e., position of the εcm rot (ω) maximum, increases by
two orders of magnitude from ω ≈ 10−4 ps−1 (f ≈ 0.016 GHz) at 300 K to ω = 10−2 ps−1 (f = 1.6 GHz) at 500 K. The zero-frequency value of the real part of εcm rot (ω) decreases mono0 tonically from εcm rot (0) ≈ 11.1 to 5.6 in the same temperature range, leading to the lowering
trend of the overall static dielectric constant of BMI+ PF− 6 with T . These results indicate that ion reorientational dynamics undergo dramatic acceleration, while their static dipole correlation normalized by T (cf. eqs 7 and 9) becomes weakened gradually as T increases. In view of the temperature dependence of dielectric relaxation in conventional dipolar solvents, this trend is precisely what is expected. To gain additional insight, we have examined reorientational dynamics of collective and single-ion center-of-mass dipole moments. Irrespective of T , Φcm MM (t) in Figure 2a is characterized by fast initial relaxation, followed by a slow decay. As expected, relaxation of Φcm MM (t) shows pronounced acceleration with growing T . The normalized self-correlation function of cation center-of-mass dipoles cm Cµµ (t) =
X
.X h µcm,α (t) · µcm,α i h µ2cm,β i ,
α ∈+
(10)
β ∈+
in Figure 2b exhibits a similar behavior. These results indicate that rotational friction for RTIL ions and thus viscosity decrease markedly as T increases. In eq 10, α ∈ + denotes that cm sum is over all cations. It is noteworthy that both Φcm MM (t) and Cµµ (t) show a significant
departure from a single exponential decay, disclosing that BMI+ PF− 6 is not a Debye solvent. Using a tri-exponential function to fit the slowly-decaying part of Φcm MM (t), viz., its time evolution for 2 ps < t < 5 ns, we analyzed its relaxation time Z ∞ cm rot dt Φcm τM = MM (t)/ΦMM (0) .
(11)
0 rot The results are compiled in Table 1. τM drops sharply with T ; it decreases by two orders of rot magnitude from τM ≈ 9 ns to 90 ps as T rises from 300 K to 500 K. This dramatic speed-up in
the system dipole relxation, resulting from huge acceleration of ion reorientations with T , is 00 responsible for the shift of the εcm rot (ω) maximum from f ≈ 0.016 GHz at 300 K to f = 1.6 GHz
at 500 K in Figure 1a. We also note that the initial value of Φcm MM (t) normalized by T , i.e., 2 Φcm MM (t)/T at t = 0, decreases monotonically from 13.9 to 8.9 D /K as T increases from 300 K
to 500 K (cf. Figure 2a). This trend, arising primarily from its T factor, is responsible for 0 the reduction of εcm rot (0) with T as mentioned above (cf. eq 7).
6
The probability distribution of the center-of-mass dipole moment of BMI+ ions is displayed in Figure 3. Two peaks of the distribution arise from two different conformations of the cation butyl group, viz., gauche-anti and anti-anti conformations of its dihedrals N-C-C-C and C-C-C-C.75–79 The peak associated with the gauche-anti conformation becomes somewhat weakened and broadened with growing T , indicating its destabilization with respect to the anti-anti conformation. Nevertheless the overall feature of the probability distribution remains essentially the same in the entire temperature range we have investigated. The average and average square center-of-mass dipole moment are 5.8 D and 34 D2 regardless of T . This is expected since the Φcm MM (t) value at t = 0 does not vary much with T (see Figure 2a). We turn to εcm tr (ω) in Figure 1b. The DC conductivity needed in eq 9 was determined via the Green-Kubo (GK) formula (cf. eqs 2 and 7) 1 σ(0) = −i lim ω χ(ω) = ω→0 3V kB T
Z
∞
dt Φcm JJ (t) ,
(12)
0
where σ(0) was obtained as the plateau value80, 81 of the time integration of Φcm JJ (t). Dielectric 10 ps−1 . Both of them are characterized by two pronounced bands at frequency range f ∼ f ≈ 12 and 25 ps−1 plus peak structures of lower intensity at higher frequencies. According to our prior analysis of CE (t),69 PF− 6 ions play a major role in the two bands at f ≈ 12 and 25 ps−1 with minor contributions from BMI+ cations, while structures at higher frequencies > 27 ps−1 ) arise exclusively from the cations. It is noteworthy that peak positions (i.e., f ∼ are rather insensitive to T although their intensity tends to decrease.
5
CONCLUDING REMARKS
In this article, we have studied dielectric properties of 1-butyl-3-methylimidazolium hexafluorophosphate via MD, focusing on their variations with temperature. The static dielectric constant of BMI+ PF− 6 was found to decrease slowly with T , consonant with experimental results for various imidazolium-based ionic liquids. The weak T -dependence was attributed to opposing effects of ion translations and reorientations, which tend to raise and lower ε0 , respectively, as T increases. One notable consequence of this is that as T grows, ion translations play a progressively more significant role, so that its contribution to ε0 at elevated temperatures becomes nearly comparable to that of ion reorientations. Ion translational and reorientational dynamics yield dielectric loss in the far-IR and microwave regions, respectively. It was found that the location of the bi-modal far-IR band changes little with T ; the position of its tera-Hertz component arising from hindered inertial translations downshifts somewhat while its dissipative subtera-Hertz mode remains essentially unchanged. The former trend is ascribed to the persistence of tight inter-ionic structures in BMI+ PF− 6 in a wide temperature range. The librational frequency of the hindered translational motions of ions under these structures does not change much as T is varied. By contrast, the absorption band in the microwave region shows a pronounced blue-shift due to the acceleration of ion reorientational dynamics with T . The intensity of the far-IR and microwave absorption bands increases and decreases, respectively, as T rises. Our findings on dielectric relaxation are in reasonable accord with recent measurements with different RTILs.90 We have also examined the influence of T on equilibrium solvation dynamics. As T increases, their subpicosecond inertial dynamics become, in general, slower but only slightly. Analogous to dielectric relaxation, this trend was attributed to tight solute-ion structures that do not change significantly with temperature. As expected, the slow dissipative relaxation of solvent fluctuation dynamics becomes accelerated as T grows.
14
While our analysis is confined to BMI+ PF− 6 , we expect that roles of hindered translations and reorientations of ions will remain mostly the same for many other ionic liquid systems. Therefore clear distinction in the temperature behaviors of the two motions found here will be useful in obtaining molecular-level understanding of dynamic properties of RTILs, accessible via various spectroscopies.
ACKNOWLEDGMENT This work was motivated by the comments made by Professor Hermann Weing¨artner at the Symposium on the Physical Chemistry of Ionic Liquids during the 239th ACS National Meeting in San Francisco. This work was supported in part by the National Science Foundation through NSF Grant No. CHE-1223988.
15
Table 1: MD results a)
a)
˙ 2i h(∆E)
ωs
τs
rot τM
37.4
94000
50.2
304
9.1
51.5
103000
44.7
157
1.4
85.2
64.7
118000
42.7
34.5
0.30
0.310; 0.250
83.1
69.8
128000
42.9
10.4
0.13
0.370; 0.300
82.1
74.9
138000
42.9
4.69
0.089
T
ε0 b),c)
σ(0) b)
h∆Ei
h(δ∆E)2 i
300
12.8 (11.1+1.7); 13.0 (11.1+1.9)
0.040; 0.010
87.2
350
10.7 (8.4+2.3); 11.0 (8.4+2.6)
0.080; 0.040
85.3
400
10.5 (7.9+2.6); 11.0 (7.9+3.1)
0.180; 0.120
450
9.3 (6.6+2.7); 9.8 (6.6+3.2)
500
8.3 (5.6+2.7); 8.9 (5.6+3.3)
Units for T , ∆E, ∆E˙ and σ(0) are K, kcal mol−1 and kcal mol−1 ps−1 and S/m, respectively.
rot ωs , τs and τM are the solvent frequency (ps−1 ), solvation time (ps) and M cm rot relaxation time
(ns). b)
The first and second data sets are the results obtained using, respectively, the Green-Kubo
0 and Einstein-Helfand methods for σ(0) and εcm tr (0). c)
0 cm 0 The first and second numbers in the parentheses are the εcm rot (0) and εtr (0) values, respec-
cm 0 tively. Due to slow convergence of hM cm rot i at 300 K, the εrot (0) result at this temperature is
not as accurate as other cases.
16
References [1] Weing¨artner, H.; Knocks, A.; Schrader, W.; Kaatze, U. J. Phys. Chem. A 2001, 105, 8646. [2] Wakai, C.; Oleinikova, A.; Ott, M.; Weing¨artner, H. J. Phys. Chem. B 2005, 109, 17028. [3] Daguenet, C.; Dyson, P. J.; Krossing, I.; Oleinikova, A.; Slattery, J.; Wakai, C.; Weing¨artner, H. J. Phys. Chem. B 2006, 110, 12682. [4] Schr¨odle, S.; Annat, G.; MacFarlane, D. R.; Forsyth, M.; Buchner, R.; Hefter, G. Chem. Commun. 2006, 1748. [5] Stoppa, A.; Hunger, J.; Buchner, R.; Hefter, G.; Thoman, A.; Helm, H. J. Phys. Chem. B 2008, 112, 4854. [6] Hunger, J.; Stoppa, A.; Schr¨odle, S.; Hefter, G.; Buchner, R. Chem. Phys. Chem. 2009, 10, 723. [7] Mizoshiri, A.; Nagao, T.; Mizoguchi, Y.; Yao, M. J. Chem. Phys. 2010, 132, 164510. [8] Huang, M.; Jiang, Y.; Sasisanker, P.; Driver, G. W.; Weingartner, H. J. Chem. Eng. Data 2011, 56, 1494. [9] Hunger, J.; Stoppa, A.; Buchner, R. J. Phys. Chem. B 2009, 113, 9527. [10] Yamamoto, K.; Tani, M.; Hangyo, M. J. Phys. Chem. B, 2007, 111, 4854. [11] Chakraborty, A.; Inagaki, T.; Banno, M.; Mochida, T.; Tominaga, K. J. Phys. Chem. A 2011, 115, 1313. [12] Kr¨ uger, M.; Br¨ undermann, E.; Funkner, S.; Weing¨artner, H.; Martina Havenith, H. J. Chem. Phys. 2010, 132, 101101. [13] Turton, D. A.; Hunger, J.; Stoppa, A.; Hefter, G.; Thoman, A.; Walther, M.; Buchner, R.; Wynne, K. J. Am. Chem. Soc. 2009, 131, 11140. [14] Schr¨oder, C.; Rudas, T.; Steinhauser, O. J. Chem. Phys. 2006, 125, 244506. [15] Schr¨oder, C.; Wakai, C.; Weing¨artner, H.; Steinhauser, O. J. Chem. Phys. 2007, 126, 084511. 17
[16] Schr¨oder, C.; Rudas, T.; Neumayr, G.; Gansterer, W.; Steinhauser, O. J. Chem. Phys. 2007, 127, 044505. [17] Schr¨oder, C.; Haberler, M.; Steinhauser, O. J. Chem. Phys. 2008, 128, 134501. [18] Shim, Y.; Kim, H. J. J. Phys. Chem. B 2008, 112, 11028. [19] Schr¨oder, C.; Hunger, A.; Stoppa, R.; Steinhauser, O. J. Chem. Phys. 2008, 129, 184501. [20] Schr¨oder, C.; Steinhauser, O. J. Chem. Phys. 2009, 131, 114504. [21] Schr¨oder, C. J. Chem. Phys. 2011, 135, 024502. [22] Yamaguchi, T.; Koda, S. J. Mol. Liq. 2011, 164, 49. [23] Halder, M.; Headley, L. S.; Mukherjee, P.; Song, X.; Petrich, J. W. J. Phys. Chem. A 2006, 110, 8623. [24] Arzhantsev, S.; Jin, H.; Baker, G. A.; Maroncelli, M. J. Phys. Chem. B 2007, 111, 4978. [25] Jin, H.; Baker, G. A.; Arzhantsev, S.; J.; Dong, S.; Maroncelli, M. J. Phys. Chem. B 2007, 111, 7291. [26] Kashyap, H. K.; Biswas, R. J. Phys. Chem. B 2008, 112, 12431. [27] Song, X. J. Chem. Phys. 2009, 131, 044503. [28] Xiao, T.; Song, X. J. Chem. Phys. 2011, 135, 104104. [29] Maroncelli, M.; Zhang, X.-X.; Liang, M.; Roy, D.; Ernsting, N. P. Faraday Discuss. 2012, 154, 409. [30] Zhang, X.-X.; Liang, M.; Ernsting, N. P.; Maroncelli, M. J. Phys. Chem. B 2013, 117, 4291. [31] Zhang, X.-X.; Schr¨oder, C.; Ernsting, N. P. J. Chem. Phys. 2013, 138, 111102. [32] Zhang, X.-X.; Liang, M.; Ernsting, N. P.; Maroncelli, M. J. Phys. Chem. Lett. 2013, 4, 1205.
18
[33] Kosower, E. M. An Introduction to Physical Organic Chemistry; Wiley: New York, 1968. [34] Reichardt, C. Solvents and Solvent Effects in Organic Chemistry, 2nd ed.; VCH: Weinheim, 1988. [35] Reichardt, C. Chem. Rev. 1994, 94, 2319. [36] Carmichael, A. J.; Seddon, K. R. J. Phys. Org. Chem. 2000, 13, 591. [37] Aki, S. N. V. K.; Brennecke, J. F.; Samanta, A. Chem. Commun. 2001, 413. [38] Muldoon, M. J.; Gordon, C. M.; Dunkin, I. R. J. Chem. Soc. Perkin Trans. 2 2001, 433. [39] Baker, S. N.; Baker, G. A.; Bright, F. V. Green Chem. 2002, 4, 165. [40] Fletcher, K. A.; Storey, I. K.; Hendricks, A. E.; Pandey, S.; Pandey, S. Green Chem. 2002, 3, 210. [41] Karmakar, R.; Samanta, A. J. Phys. Chem. A 2002, 106, 4447. [42] Ingram, J. A.; Moog, R. S.; Ito, N.; Biswas, R.; Maroncelli, M. J. Phys. Chem. B 2003, 107, 5926. [43] Karmakar, R.; Samanta, A. J. Phys. Chem. A 2003, 107, 7340. [44] Lu, J.; Liott C. L.; Eckert, C. A. J. Phys. Chem. A 2003, 107, 3995. [45] Reichardt, C. Green Chem. 2005, 7, 339. [46] Shim, Y.; Duan, J.; Choi, M. Y.; Kim, H. J. J. Chem. Phys. 2003, 119, 6411. [47] Shim, Y.; Choi, M. Y.; Kim, H. J. J. Chem. Phys. 2005, 122, 044510. [48] Shim, Y.; Jeong, D.; Manjari, S. R.; Choi, M. Y.; Kim, H. J. Acc. Chem. Res. 2007, 40, 1130. [49] Krossing, I.; Slattery, J. M.; Daguenet, C.; Dyson, P. J.; Oleinikova, A.; Weing¨artner, H. J. Am. Chem. Soc. 2006, 128, 13427. [50] Shim, Y.; Choi, M. Y.; Kim, H. J. J. Chem. Phys. 2005, 122, 044511.
19
[51] Kobrak, M. N. J. Chem. Phys. 2006, 125, 064502. [52] Kobrak, M. N. J. Chem. Phys. 2007, 127, 184507. [53] Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. J. Phys. Chem. B 2004, 108, 16593. [54] Widegren, J. A.; Saurer, E. M.; Marsh, K. n.; Magee, J. W. J. Chem. Thermodyn. 2005, 37, 569. [55] Kanakubo, M.; Harris, K. R.; Tsuchihashi, N.; Ibuki, K.; Ueno, M. J. Phys. Chem. B 2007, 111, 2062. [56] Stoppa, A.; Hunger, J.; Buchner, R. J. Chem. Eng. Data 2009, 54, 472. [57] Hubbard, J. B.; Colonomos, P.; Wolynes, P. G. J. Chem. Phys. 1979, 71, 2652. [58] Caillol, J. M.; Levesque, D.; Weis, J. J. J. Chem. Phys. 1986, 86, 6645. [59] See, e.g.: Friedman, H. L. A Course in Statistical Mechanics; Prentice-Hall: Englewood Cliffs, 1985. [60] Lopes, J. N. C.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 2038. [61] Lopes, J. N. C.; Deschamps, J.; Padua, A. A. H. J. Phys. Chem. B 2004, 108, 11250. [62] Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225. [63] Jorgensen, W. L.; McDonald, N. A. Theochem, 1998, 424, 145. [64] Kaminski, G.; Jorgensen, W. L. J. Chem. Soc. Perkin Trans. 2 1999, 23, 65. [65] Cheatham III, T. E.; Young, M. A. Biopolymers, 2001, 56, 232. [66] Ponder, J. W.; Case, D. A. Adv. Prot. Chem. 2003, 66, 27. [67] Case, D. A.; Cheatham III, T. E.; Darden, T.; Gohlke, H.; Luo, R.; Merz Jr., K. M.; Onufriev, A.; Simmerling, C.; Wang, B.; Woods, R. J. Comp. Chem. 2005, 26, 1668. [68] Liu, Z. P.; Huang, S. P.; Wang, W. C. J. Phys. Chem. B 2004, 108, 12978. [69] Shim, Y.; Kim, H. J. J. Phys. Chem. B 2010, 114, 10160. 20
[70] Jeong, D.; Shim, Y.; Choi, M. Y.; Kim, H. J. J. Phys. Chem. B 2007, 111, 4920. [71] Forster, T. R.; Smith, W. The DL POLY 2.13 Reference Manual;Warington, CCLRC, Daresbury Laboratory, 2001. [72] Heyes, D. M. J. Chem. Phys. 1982, 74, 1924. [73] Pereiro, A. B.; Legido, J. L.; Rodriguez, A. J. Chem. Thermodyn. 2007, 39, 1168. [74] Y. Huo, S. Xia, P. Ma, J. Chem. Eng. Data 52, 2077 (2007). [75] Holbrey, J. D.; Reichert, W. M.; Nieuwenhuyzen, M.; Johnston, S.; Seddon, K. R.; Rogers, R. D. Chem. Commun. 2003, 1636. [76] Ozawa, R.; Hayashi, S.; Saha, S.; Kobayashi, A.; Hamaguchi, H. Chem. Lett. 2003, 32, 948. [77] Berg, R. W.; Deetlefs, M.; Seddon, K. R.; Shim, I.; Thompson, J. M. J. Phys. Chem. B 2005, 109, 19018. [78] Lopes, J. N. A. C.; P´adua, A. A. H. J. Phys. Chem. B 2006, 110, 7485. [79] Chang, H.-C.; Jiang, J.-C.; Su, J.-C.; Chang, C.-Y.; Lin S. H. J. Phys. Chem. A 2007, 111, 9201. [80] Kirkwood, J. J. Chem. Phys. 1946, 14, 180. [81] Chandler, D. J. Chem. Phys. 1978, 68, 2959. [82] Margulis, C. J.; Stern, H. A.; Berne, B. J. J. Phys. Chem. B 2002, 106, 12017. [83] Del P´opolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 1744. [84] Rey-Castro, C.; Vega, L. F. J. Phys. Chem. B 2006, 110, 14426. [85] Hu, Z.; Huang, X.; Annapureddy, H. V. R.; Margulis, C. J. J. Phys. Chem. B, 2008, 112, 7837. [86] Shirota, H.; Castner, Jr., E. W. J. Phys. Chem. A 2005, 109, 9388. [87] Rajian, J. R.; Li, S.; Bartsch, R. A.; Quitevis, E. L. Chem. Phys. Lett. 2004, 393, 372. [88] Shirota, H.; Castner, Jr., E. W. J. Phys. Chem. B 2005, 109, 21576. 21
[89] Bhargava, B. L.; Balasubramanian, S. J. Chem. Phys. 2005, 123, 144505. [90] Turton, D. A.; Sonnleitner, T.; Ortner, A.; Walther, M.; Hefter,G.; Seddon, K. R.; Stana, S.; Plechkova, N. V.; Buchner, R.; Wynne, K. Faraday Discuss. 2012, 154, 145. [91] Yan, T.; Burnham, C. J.; Del P¨opolo, M. G.; Voth, G. A. J. Phys. Chem. B 2004, 108, 11877. [92] Borodin, O. J. Phys. Chem. B 2009, 113, 11463. [93] Chitanvis, S. M. J. Chem. Phys. 1996, 104, 9065. [94] Jeon, J.; Kim, H. J. J. Solution Chem. 2001, 30, 849. [95] Jeon, J.; Kim, H. J. J. Chem. Phys. 2003, 119, 8626. [96] Abbound, J. M.; Douhal, A.; Ar´ın, M. J.; Diez, M. T.; Homan, H.; Guih´eneuf, G. J. Phys. Chem. 1989, 93, 214. [97] Schuddeboom, W.; Jonker, S. A.; Warman, J. M.; Leinhos, U.; K¨ uhnle, W.; Zachariasse, K. A. J. Phys. Chem. 1992, 96, 10809. [98] Il’ichev, Y. Y.; K¨ uhnle, W.; Zachariasse, K. A. J. Phys. Chem. A 1998, 102, 5670. [99] Asahi, T.; Ohkohchi, M.; Matsusaka, R.; Mataga, N.; Zhang, R. P.; Osuka, A.; Maruyama, K. J. Am. Chem. Soc. 1993, 115, 5665. [100] Read, I.; Napper, A.; Kaplan, R.; Zimmt, M. B.; Waldeck, D. H. J. Am. Chem. Soc. 1999, 121, 10976. [101] Jeon, J.; Kim, H. J. J. Phys. Chem. A 2000, 104, 9812. [102] Dorairaj, S.; Kim, H. J. J. Phys. Chem. A 2002 106, 2322. [103] Shim, Y.; Kim, H. J. J. Phys. Chem. B 2007, 111, 4510. [104] The NP and IP states were referred to as NP3.5 and DP3.5 in ref 69, respectively. [105] Kashyap, H. K.; Biswas, R. J. Phys. Chem. B 2010, 114, 16811. [106] Liptay, W. In Excited States, Vol. 1; Lim, E. C., Ed.; Academic: New York, 1974. [107] Kim, H. J. J. Chem. Phys. 1996, 105, 6883. 22
[108] Beens, H.; Weller, A. In Organic Molecular Photophysics, Vol. 2; Birks, J. B., Ed.; Wiley: London, 1975. [109] Mataga, N. In The Exciplex; Gordon, M., Ware, W. R., Eds.; Academic: New York, 1975. [110] Mataga, N. In Molecular Interactions, Vol 2; Ratajczak, H., Orville-Thomas, W. J., Eds.; Wiley: Chichester, 1981. [111] Roy, D.; Maroncelli, M. J. Phys. Chem. B 2012, 116, 5951. [112] Edwards, D. M. F.; Madden, P. A.; McDonald, I. R. Mol. Phys. 1984, 111, 1141. [113] Manjari, S. R.; Kim, H. J. J. Chem. Phys. 2005, 123, 014504. [114] Margulis, C. J. Mol. Phys. 2004, 102, 829. [115] Kobrak, M. N.; Znamenskiy, V. Chem. Phys. Lett. 2004, 395, 127. [116] Hu, Z.; Margulis, C. J. Proc. Natl. Acad. Sci. 2006, 103, 831. [117] Jeong, D.; Choi, M. Y.; Jung, Y.; Kim, H. J. J. Chem. Phys. 2008, 128, 174504.
23
15 (a) 10 εcm rot (ω)
4
300K 350K 400K 450K 500K
(b) 3 ε cm tr (ω)
5
2 1 0
0
0.0001 0.01 1 -1 ω (ps )
-1
100
15
0.0001 0.01 1 -1 ω (ps )
100
6 (d)
(c) 10
3
σ(ω)
εc (ω)
(S/m)
5 0
0.0001 0.01 1 -1 ω (ps )
100
0
-3
0
10 20 30 40 50 -1 ω (ps )
Figure 1: MD results for frequency-dependent dielectric constant and conductivity of cm cm BMI+ PF− 6 : (a) εrot (ω); (b) εtr (ω); (c) εc (ω); (d) σ(ω). The solid and dotted lines rep-
resent the real and imaginary parts of the susceptibility, respectively. In (d), the results for the Drude model σ(ω) ∝ i(ω + i/τ )−1 with τ = 0.1 ps are plotted in black.
24
5000
(a)
4000 Φcm MM(t)
3000
1
300K 350K 400K 450K 500K
(b) 0.95 cm (t) Cµµ
2000
0.9 300K 350K 400K 500K 0.85 0 0.5
1000 0 0
0.2 0.4 0.6 0.8 t (ns)
1
1 t (ps)
1.5
2
− + cm Figure 2: MD results for time correlation functions (a) Φcm MM (t) and (b) Cµµ (t) in BMI PF6 . 2 The initial values of Φcm MM (t) in (a) are ∼ 3920, 4250, 4310, 4330, 4140 D at T = 300, 350,
400, 450 and 500 K, respectively.
0.8 300K 400K 0.6 500K P(µcm)
0.4 0.2 0
3
4
5 6 µcm
7
8
Figure 3: Probability distribution of the center-of-mass dipole moment of BMI+ . Two peaks centered around 5.3 D and 6.2 D arise from the gauche-anti and anti-anti conformations of the cation butyl group, respectively.
25
120
300K 350K 400K 450K 500K
80 cm ΦJJ(t)/T
40 0
-40
0
0.2 0.4 0.6 0.8 t (ps)
1
− 2 −2 + Figure 4: Time correlation function Φcm JJ (t) (units: D ps ) normalized by T in BMI PF6 . cm The initial value of Φcm JJ (t)/T does not vary with T because ΦJJ (0) is proportional to the ion
translational kinetic energy (cf. eq 8).
12
300K 500K
(a)
10 PMF (kcal/mol)
3
2 g(r) 1
300K 500K
(b)
8 6 4 2 0
0
0.5
1 r (nm)
1.5
-2
0.5
1 r (nm)
1.5
Figure 5: (a) Cation-anion radial distribution function and (b) its potential of mean force. The center-of-mass is employed to describe ion positions.
26
14 dielectric constant
12 ε0
10 8 6
εcm rot (0)
4 2 0
εcm tr (0) 300 350 400 450 500 T (K)
Figure 6: Static dielectric constant ε0 of BMI+ PF− 6 and its translational and reorientational cm components εcm tr (0) and εrot (0) in eq 9. The solid and dotted lines represent the results
obtained with the EH and GK methods, respectively.
27
1
1
300K 350K 400K 450K 500K
(a) 0.8 0.6 CE(t)
(b)
CM(t)
0.4 0.2 0.9 0
0
5
0.5
1 t (ps)
1.5
2
0
~
4
3
~
CM(f)
2 1 0
1 t (ps)
1.5
2
5
(c)
4 CE(f)
0.5
(d)
3 2 1
20 40 -1 f (ps )
0
60
20 40 -1 f (ps )
60
Figure 7: Time correlation functions CE (t), CM (t) and their power spectra C˜E (f ) and C˜M (f ) in BMI+ PF− 6 . CE (t) is obtained in the presence of the IP solute.
28
12
8 g(r) 6 4
4 2 0
2 0
300K 350K 400K 450K 500K
(b)
6
PMF (kcal/mol)
(a)
10
8
300K 350K 400K 450K 500K
-2 2
4
6
8 r
10 12 14
2
4
6
8 r
10 12 14
7
(c)
6 5
ln τs
4 3 2 1 0
Ea=6.45(kcal/mol) 2
2.5
3
-1
3.5
1000/T (K ) Figure 8: (a) Radial distribution of anions around the positively charged site of the IP solute, (b) its potential of mean force, and (c) solvation time τs in BMI+ PF− 6 . The center-of-mass is employed to describe anion positions in (a) and (b).
29
